Calculating the value of a bond

CFA Level II Fixed Income
#1

Consider a 4.5% bond maturing in five years, which is currently callable at 100. On a 4% flat yield curve at 15% volatility.

The value of this is 99.75. Can anyone help explaining how!

My solution was N=5, I/Y = 4, PMT = 4.5, FV = 100… This way the PV comes out to 102.23.

I think this has got to do with interest rate volatility of 15%. But how can I compute the value? Am I supposed to calibrate the rates from f(1,1) to f(4,1)… using the spots S1=4 to S5=4?, . Making a binomial interest rate tree for 5 years with 15% volatility?

#2

You have to build a binomial tree.

Sorry.

#3

Hello Siidheart,

Your approach was wrong. You can’t value a bond with an embedded option using a financial calculator, except by setting up a binomial tree. The approach you used is only suitable for valuing bonds without any embedded option, i.e., straight bonds.

Hope you found this helpful. Cheers.

#4

It is painful to build a binomial tree for 5 years frown …by hand calculations. I hope this won’t show up in the real exam (touch wood).

#5

It won’t.

(By the way, for anything greater than 4 periods, it’s not merely difficult, it’s impossible (analytically). You have to approximate it numerically.)

#6

The exam is probably just going to give us 2 or 3 years. I’m guessing mostly 3, as is in the textbook.

#7

That’s pretty interesting–could you expatiate a bit?